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Simplifying 3(4x + -3) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 2 + -1x Reorder the terms: 3(-3 + 4x) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 2 + -1x (-3 * 3 + 4x * 3) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 2 + -1x (-9 + 12x) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 2 + -1x Multiply (1 + 2x) * (1 + 2x) -9 + 12x + 4(1(1 + 2x) + 2x * (1 + 2x)) = 16(x + -2) * 2 + -1x -9 + 12x + 4((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 16(x + -2) * 2 + -1x -9 + 12x + 4((1 + 2x) + 2x * (1 + 2x)) = 16(x + -2) * 2 + -1x -9 + 12x + 4(1 + 2x + (1 * 2x + 2x * 2x)) = 16(x + -2) * 2 + -1x -9 + 12x + 4(1 + 2x + (2x + 4x2)) = 16(x + -2) * 2 + -1x Combine like terms: 2x + 2x = 4x -9 + 12x + 4(1 + 4x + 4x2) = 16(x + -2) * 2 + -1x -9 + 12x + (1 * 4 + 4x * 4 + 4x2 * 4) = 16(x + -2) * 2 + -1x -9 + 12x + (4 + 16x + 16x2) = 16(x + -2) * 2 + -1x Reorder the terms: -9 + 4 + 12x + 16x + 16x2 = 16(x + -2) * 2 + -1x Combine like terms: -9 + 4 = -5 -5 + 12x + 16x + 16x2 = 16(x + -2) * 2 + -1x Combine like terms: 12x + 16x = 28x -5 + 28x + 16x2 = 16(x + -2) * 2 + -1x Reorder the terms: -5 + 28x + 16x2 = 16(-2 + x) * 2 + -1x Reorder the terms for easier multiplication: -5 + 28x + 16x2 = 16 * 2(-2 + x) + -1x Multiply 16 * 2 -5 + 28x + 16x2 = 32(-2 + x) + -1x -5 + 28x + 16x2 = (-2 * 32 + x * 32) + -1x -5 + 28x + 16x2 = (-64 + 32x) + -1x Combine like terms: 32x + -1x = 31x -5 + 28x + 16x2 = -64 + 31x Solving -5 + 28x + 16x2 = -64 + 31x Solving for variable 'x'. Reorder the terms: -5 + 64 + 28x + -31x + 16x2 = -64 + 31x + 64 + -31x Combine like terms: -5 + 64 = 59 59 + 28x + -31x + 16x2 = -64 + 31x + 64 + -31x Combine like terms: 28x + -31x = -3x 59 + -3x + 16x2 = -64 + 31x + 64 + -31x Reorder the terms: 59 + -3x + 16x2 = -64 + 64 + 31x + -31x Combine like terms: -64 + 64 = 0 59 + -3x + 16x2 = 0 + 31x + -31x 59 + -3x + 16x2 = 31x + -31x Combine like terms: 31x + -31x = 0 59 + -3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.6875 + -0.1875x + x2 = 0 Move the constant term to the right: Add '-3.6875' to each side of the equation. 3.6875 + -0.1875x + -3.6875 + x2 = 0 + -3.6875 Reorder the terms: 3.6875 + -3.6875 + -0.1875x + x2 = 0 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + -0.1875x + x2 = 0 + -3.6875 -0.1875x + x2 = 0 + -3.6875 Combine like terms: 0 + -3.6875 = -3.6875 -0.1875x + x2 = -3.6875 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = -3.6875 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = -3.6875 + 0.0087890625 Combine like terms: -3.6875 + 0.0087890625 = -3.6787109375 0.0087890625 + -0.1875x + x2 = -3.6787109375 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = -3.6787109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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